分布时滞随机偏微分系统的均方指数稳定性  

Mean-square exponential stability of stochastic partial differential systems with distributed time-delay

作　　者：李延波 陈超洋[2,3] 张晶华 李成群 LI Yan-bo;CHEN Chao-yang;ZHANG Jing-hua;LI Cheng-qun(School of mathematics and quantitative economics,Guangxi University of Finance and Economics,Nanning Guangxi 530001,China;School of Information and Electrical Engineering,Hunan University of Science and Technology,Xiangtan Hunan 411201,China;Shenzhen Institutes of Advanced Technology,Chinese Academy of Sciences,Shenzhen Guangdong 518055,China)

机构地区：[1]广西财经学院数学与数量经济学院,广西南宁530001 [2]湖南科技大学信息与电气工程学院,湖南湘潭411201 [3]中国科学院深圳先进技术研究院,广东深圳518055

出　　处：《控制理论与应用》2022年第11期2185-2192,共8页Control Theory & Applications

基　　金：国家重点研发计划国际科技创新合作项目(2019YFE0118700);国家自然科学基金项目(61973110,71961002);湖南省杰出青年基金项目(2021JJ10030);湖南省湖湘青年英才科技创新人才项目(2020RC3048);广西财经学院博士科研启动项目(BS2019002);统计学广西一流学科建设项目(2022SXYB03);广西青年扩展项目(2020KY16018);数字制造装备与技术国家重点实验室开放基金资助项目(DMETKF2022023)资助。

摘　　要：针对一类同时具有分布时滞和维纳过程的随机偏微分系统,首先基于ItÔ微分公式,通过计算弱无穷小算子,得到了随机微分导数;其次利用Green公式和积分不等式及Schur补引理对矩阵不等式进行处理;然后对微分两边积分并同时取数学期望处理随机交叉项;获得了分布时滞随机偏微分系统是均方指数稳定的充分条件.在此基础上,进一步考虑了离散变时滞和分布变时滞在一定约束情形下的分布时滞随机偏微分系统的均方指数稳定性问题.最后给出仿真实例,仿真结果表明所获得的线性矩阵不等式条件保证了系统的稳定性,验证了所得结论的有效性.The sufficient conditions for mean-square exponential stability of stochastic partial differential system with distributed delays and Wiener processes are given. First of all, the stochastic differential derivative is obtained by calculating weak infinitesimal operator based on the ItÔ differential formula. Secondly, the matrix inequality is handled by the Green formula, the integral inequality and the Schur complement lemma. Then, both sides of the differential are integrated and mathematical expectation is taken to deal with the random cross term at the same time. On this basis, the mean-square exponential stability of distributed delay stochastic partial differential systems with discrete and distributed time-varying delay under certain constraints is further considered. Finally, a simulation example is given. The simulation results show the obtained linear matrix inequality conditions ensure the stability of the system and verify the effectiveness of the conclusions.

关 键 词：随机偏微分系统 分布时滞 ItÔ公式 均方指数稳定性 

分 类 号：O175[理学—数学]